Complex contact structures and the first eigenvalue of the Dirac operator on Kähler manifolds

DOI10.1007/BF01895834zbMath0855.53026OpenAlexW2067971024MaRDI QIDQ1895261

Klaus-Dieter Kirchberg, Uwe Semmelmann

Publication date: 17 February 1997

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58203

zbMATH Keywords

Dirac operatorKähler manifoldfirst eigenvaluecomplex contact structure

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Related Items (2)

Eigenvalue estimates for generalized Dirac operators on Sasakian manifolds ⋮ Spin\(^{c}\) geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian sub\-manifolds

Cites Work

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• 7-dimensional compact Riemannian manifolds with Killing spinors
• Spectrum of the Dirac operator on complex projective space \(P_{2q- 1}({\mathbb{C}})\)
• Compact six-dimensional Kähler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator
• An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature
• Quaternionic Kaehler manifolds
• Killing spinors on Kähler manifolds
• Clifford modules
• Characterizations of complex projective spaces and hyperquadrics
• Remarks on Complex Contact Manifolds
• Some Further Properties of Kählerian Twistor Spinors

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